S. Keel, F. Herzog, and H.P. Geering (Switzerland)
Investment Models, Stochastic Control, Hedge Funds, Op timization, Portfolio Management
In this paper, the problem of portfolio construction includ ing alternative investments, e.g., hedge funds, is analyzed and solved for an investor having a constant relative risk aversion utility function. The investment opportunities are modelled in a framework of continuous-time stochastic dif ferential equations. In a first step, the general solution for an arbitrary number of risky investment opportunities as well as an arbitrary number of risk factors is presented. The general solution is used to derive the explicit solution for a typical investor. The typical investor, in this context, has three risk-bearing investment opportunities. These are the stock market, the bond market, and the alternative invest ment universe. The fixed income part is modelled by a short rate model. For the market portfolio, the usual geometric Brownian motion model is used. For the alternative invest ment, we use a model with the Greek letters and as in Sharpe's capital asset pricing model. The resulting optimal asset allocation law is then analyzed for typical values.
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